ASSESSMENT OF GROUNDWATER RESOURCES IN NORTHEASTERN SINAI PENINSULA CONSTRAINED BY MATHEMATICAL MODELING TECHNIQUES.

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1 Study area Fifteenth International Water Technology Conference, IWTC , Alexandria, Egypt 1 ASSESSMENT OF GROUNDWATER RESOURCES IN NORTHEASTERN SINAI PENINSULA CONSTRAINED BY MATHEMATICAL MODELING TECHNIQUES. M. A. El Samanoudi 1, G. S. Ebid 2,Nabil N. Rofail, Y. L. Ismail 4, S. A. F. Hawash 1 Faculty of Engineering, Ain Shams University, melsamanoudi@yahoo.com 2 Faculty of Engineering, Ain Shams University, gsa200@hotmail.com Hydrology Department, Desert Research Center, nabilrofail@yahoo.com 4 Hydrology Department, Desert Research Center, yehiashehata@hotmail.com National Water Research Center, Mech. & Elect. Institute, saidhawash64@yahoo.com ABSTRACT The study area extended from El-Gora and its vicinities in the south to El Sheikh Zowyed and Rafah cities in the north. Quantitatively the water bearing formation in the area has been evaluated by applying the Processing Modflow for Windows (PMWIN) and modulus contour map techniques. Qualitatively, the groundwater is evaluated by an iso-salinity distribution map. The hydraulic parameters of the water bearing formations were determined and evaluated through 12 pumping tests carried out on selected drilled wells. On the other hand the ground elevation of the study area is illustrated by a Digital Elevation Model (DEM). The DEM map indicated that the investigated area lies within a low land area. Due to the depths of groundwater (46.1m 10m from the ground surface), the rainfall replenishment is nearly absent. Based on the resulting modulus contour map, the northern and northwestern portions are characterized by reasonable potentiality of groundwater. More over, the eastern and southern portions reflect limited aquifer potentials. The mathematical modeling results revealed that the recharge to the investigated aquifer is about Million m. Keywords : Hydraulic parameters, aquifers, modulus technique, processing modflow. INTRODUCTION The present work is an approach to evaluate the groundwater conditions in El- Gora and its vicinities, El Sheikh Zowyed and Rafah areas. The investigated area occupies a part of the northeastern portion of Sinai Peninsula of about 80 km 2 (Figure 1) E E N E Rafah El Arish F7 Study area N Gora airport N Legend: City Study area Fig. 1 Key map of study area Km Scale Bar

2 Fifteenth International Water Technology Conference, IWTC , Alexandria, Egypt 2 GEOMORPHOLOGIC AND GEOLOGICAL SETTING 1. Geomorphologic settings The study area characterized by desert conditions and arid conditions. This appears in a number of land features. It is represented by the accumulation of drift sand, the development of yellow desert soils and the lack of natural vegetations. The area under investigation is characterized by moderate relief with elevations varying from about sea level to less than The present landforms are developed as a result of the endogenetic (e.g. the geological structure) and the exogenetic (the climatic condition) processes. From geomorphologic point of view, Sinai Peninsula includes the following main units (Figure 2): 1 00 Mountaineous Region Foot Slopes Old Coastal Plain Young Coastal Plain Wadi Salt Marsh Modern Shore Line Scale Bar 0 10 Km Legend : Mediterranean Sea Fig. 2 Geomorphologic map of the studied area. (Modified aftertaha, 1968) 1.1 The Southern Mountainous Region; which is composed of igneous and metamorphic rocks of Pre Cambrian age The Central Table Lands; which include two plateaux: a) El Tih is composed of Cretaceous limestone, with shale and sandstones at the base (Hammad, 1980). b) El Egma Plateau, chalky carbonate rocks of Eocene age. 1.. The Mediterranean Coastal Plain; where the investigated area lies within it and extends in the entire width of northern Sinai. This unit is bounded on the north by the Mediterranean Sea and on the south by the central high lands W N Palestine 2. Geological settings There are many studies and publications on the geology of the Sinai Peninsula. The geological structure, distribution of major formations and their stratigraphy and lithology may have direct implications on the hydrogeological conditions in the area. Geologically, the study area is covered by Quaternary deposits which consist of sand dunes, old beach sand and calcareous sandstone (Kurkar Formation). The thickness of these deposits is about 80m to 100m (Jica, 1992). The Kurkar Formation is distributed along the coastal plain and their genesis is present in the shallow marine environment. The old beach sand consists mainly of fine to coarse sand which is locally digenetic sandstone and intercalated with gravel and clayey layers. This is conformably overlying the Kurkar in some places which forms an unconfined aquifer.

3 Fifteenth International Water Technology Conference, IWTC , Alexandria, Egypt 1- Structural settings: Generally the geological structure of North Sinai is divided into the following three major units (Shata, 196): 1) Central Sinai Stable Foreland. 2) North Sinai Strongly Folded Belt. ) North Sinai Foreshore Area. The Regabet El-Naam Fault is the boundary between the top two units, 1 and 2. The Structural elements were given by RIWR (1988). It is considered as a base map in the present study for detecting the main faulting and folding systems (Figure ). Digital Elevation Model (DEM): El Arish F2 F7 Legend: Fault Fold Mediterranean Sea F2 El Sheikh Zowyed 0 10 Km Scale Bar F1 F F4 F El Gora Airport Rafah F6 F8 N Fig. Major structural elements El Arish-Rafah area, North Sinai, (Compiled after RIWR, 1988). The Digital Elevation Model of the study area (DEM) is created from the digitization of the elevation points on the topographic map of the study area (Figure 4). From this map, the investigated area lies within a low land area which may reflect that the buried channels represent the main source of groundwater recharge, in addition that the depths to the groundwater are approximately deep (14. m 10 m from the ground surface). Therefore, the rainfall replenishment is nearly absent. Fig. 4 Digital Elevation Model (DEM - D) of the study area. AQUIFER SYSTEMS In order to focus some light on the hydrogeological conditions, 80 water points tapping two water bearing formations were collected (Figure & Table 1).

4 Fifteenth International Water Technology Conference, IWTC , Alexandria, Egypt 4 Mediterranean Sea N N 1.00 Airport El Gora 0.9 Legend : Drilled Well Scale Bar 0 Km E 4 10 E Fig. Distribution map of some wells of the study area. Table 1 Available basic data water points tapping the investigated aquifers. Serial Coordinates Elevation DTW Total Depth Formation No. Longitude X Latitude Y m m m Type K K All All K All K All All K K K K K All All All All K K All: Alluvial K: Kurkar 1. The alluvial aquifer The Alluvial aquifer is represented by two main lithologic facies, gravely sand and clayey sand. Both facies together with the old beach deposits constitute what we consider as an alluvial aquifer, Taha, (1968) mentioned that the aquifer can be classified into two horizons; an upper horizon dominated by coarse gravel with

5 Fifteenth International Water Technology Conference, IWTC , Alexandria, Egypt interbeds of calcareous silt, while the lower horizon proves to be water bearing. The water exists under unconfined condition. The water table slopes gently northwards. 2. The Calcareous Sandstone (Kurkar) aquifer Kurkar aquifer is a type of Calcareous sand deposits broadly distributed in the coastal plain between West El Arish and Rafah. This aquifer unit is characterized by confined to semi-confined where the depth to water varies from 16 m (well no.24) to 8 m (well no.12) from the land surface. The Kurkar aquifer is underlined by the Pre- Quaternary sediments mainly consists of shale, sandstone, and/or limestone. Also, the Kurkar is overlined by a thick bed of clays, where a confined aquifer conditions are developed. It occupies the most part of the bottom of the Quaternary in the study area. However, where the extension of the clay bed is limited, the hydraulic connection between the Kurkar aquifer and the overlying aquifer is observed. IMPACT OF THE SRUCTURAL SETTING ON GROUNDWATER OCCURRENCE The previous studies elucidated that the structural setting has a direct impact on the occurrence and flow direction of groundwater. In order to draw a general view of the hydrogeological setting of the study aquifer, two hydrogeological cross sections were drawn in Figures (6, 7, 8 & 9). These sections displayed that the groundwater occurred into two zones. The upper one (Alluvial aquifer) composed of gravely sand with interbeds of calcareous silt. This aquifer seems to be unconfined aquifer. On the other hand, the lower one (Kurkar aquifer) consists of calcareous sandstone. It overlained by thick clay bed. According to the occurrence and extension of clay layer, the Kurkar aquifer varies from unconfined to semi- confined. Mediterranean Sea B A N ' B' Airport El Gora 1 0 N 0.9 Legend : Drilled Well Scale Bar 0 Km E 4 10 E Fig. 6 Directions of the hydrogeological cross-sections.

6 Fifteenth International Water Technology Conference, IWTC , Alexandria, Egypt 6 West El Masaid Fluviomarine Kurkar aquifer Marine Kurkar aquifer Continental Kurkar aquifer East Gaza m Sea 0.00 Level A A F7 Regional groundwater flow Recent sandstone aquifer LEGEND: F m F1 Calcerous sandstone (fluviomarine kurkar aqufer, Lower Pleistocene), Delta Wadi El-Arish Calcerous sandstone (Continental kurkar aquifer, Lower Pleistocene) Loamy sand (red bed) Marine kurkar aqufer, Surface and subsurface Shelly layer (Lower Pleistocene) East El-Arish to Gaza 0 10 Km V. Scale H. Scale Local 4600 Groundwater flow F6 Regional groundwater flow Conglomerite Dark marly shale (Pliocene-Miocene) Yellow marl (Pliocene) Marly limestone Limestone Miocene Regional groundwater flow N N N To El Eḻ- Masaid N 0 00 E E Legend: Cross -Section Asphaltic Road Direction Wadi Fault E Rafah Gora airport To Gaza A' 1840 Cross-Section direction from _Masaidto El Gaza. A' Water Bearing Formation (Quaternary Aquifers): Holocene Sand dune Pleistocene continental kurkar Pleistocene Marine Kurkar Pleistocene Alluvium aquifer El Aouga Km Scale B ar Fig. 7 General trend hydrogeological cross-section from west to east Northeastern Sinai. (Compiled after Gedamy, 2004). Ground Elevation (meter) W A km H. Scale LEGEND: Well Water level Water flow Fault Sand Calcareous sandstone Limestone Clay (Kurkar Formation) 1840 E A' Fig. 8 Hydrogeological cross-section A-A'.

7 Fifteenth International Water Technology Conference, IWTC , Alexandria, Egypt NE B SW 400 B' Ground elevation (meter) B 0 1 2km H. Scale F LEGEND: Well Water level Water flow Fault Sand Calcareous sandstone Clay (Kurkar Formation) Fig. 9 Hydrogeological cross-section B-B'. B' AQUIFER PARAMETERS During the present work, an approach was made to determine and evaluate the hydraulic parameters of the water bearing formations. In order to achieve this goal, 12 pumping tests were carried out on selected drilled wells (Fig. 10). The calculated values were tabulated in Table (2) and illustrated in Figures (11, 12, 1, 14, 1, 16, 17, 18, 19 and 20). It is obvious that the alluvial deposits reflect wide range of transmissivity (4 mp2p/day 1787 mp2p/day) while, the transmissivity of marine Kurkar aquifer shows low capability of aquifer deposits to transmit water through it (144 mp2p/day 90 mp2p/day). This phenomenon could be attributed to the impact of structural setting, variation of aquifer thickness and heterogeneity of aquifer sediments. It becomes clear that the water bearing formations in the northwestern and northern portions of the study area have reasonable capability to transmit water through it. F2 Legend: 4 00 E E E Mediterranean Sea Tested well Fault 200 F F F El Gora Airport F4 F W N Palestine Scale Bar Km Fig. 10 Pumping tested-wells in the study area E 1 22 N 1 20 N 1 10 N 1 00 N

8 Fifteenth International Water Technology Conference, IWTC , Alexandria, Egypt 8 Table 2 The calculated values of hydraulic parameters of the investigated aquifers. Well No. Depth to water (m) Pumping duration (min) Total drawdown (m) Transmissivity (mp2p/ day) Time (min) t/t' Fig. 11 Analysis of pumping test Fig. 12 Analysis of recovery test data of well No data of well No Drawdown(m) Drawdown(m) Time (min) Fig. 1 Analysis of pumping test data of well No Time (min) Residual Drawdown(m) Residual Drawdown(m) t/t' Fig. 14 Analysis of recovery test data of well No t/t' Drawdown(m) Fig. 1 Analysis of pumping test data of well No Time (min) Fig. 17 Analysis of pumping test data of well No. 180 Fig. 16 Analysis of recovery test data of well No.1820 Residual Drawdown(m) t/t' Fig. 18 Analysis of recovery test data of well No.180.

9 QRnR (mpp/day) Fifteenth International Water Technology Conference, IWTC , Alexandria, Egypt 9 Drawdown(m) Time (min) Fig. 19 Analysis of pumping test data of well No Residual Drawdown(m) t/t' Fig. 20 Analysis of recovery test data of well No.1840 Aquifer potentials The modulus contour map of a groundwater aquifer can be used to evaluate the hydrologic conditions and water efficiency of the study aquifer and hence it may show character of the water balance (Rofail, 1967). The modulus of groundwater flow may be defined as the groundwater flow (either recharge or discharge) per. The modulus contour map can be calculated, for any period, from the water table map and transmissivity distribution map. This can be done by dividing each contour line of the given water table map to (n) numbers of equal parts each of width (b) meters (Sewidan and Rofail, 1972). Discharge could then be estimated using Darcy's law. The total discharge for the total length of the contour line would then be: Q = b n i= 1 TiIi Where: Q: is the total discharge for the contour line (/h) : value of transmissivity (/day) at the sector (i) : hydraulic gradient (m/m) at the sector (i) The value of the modulus groundwater flow can be calculated as the difference between the discharge values at any successive contour lines divided by the surface area between them (Table, ). The value of the modulus in this case is considered to be the mean values of the water gain or loss per unit area. The modulus coefficient -n between two contours (m) and (n) is expressed as follows: Q A m Q M (m-n) = ( m n) Where: Qm; the natural discharge at contour (m) (mpp/day) Qn; the natural discharge at contour (n) (mpp/day) Am-n;the surface area between contours m and n (kmp2p) Water Level From - To (m) Table Calculation of modulus values Discharge at Surface downstream area contour Discharge at upstream contour Qm (mpp/day) n AR(m n) (kmp2p) = QRmR Modulus value QRn AR(m n)

10 Fifteenth International Water Technology Conference, IWTC , Alexandria, Egypt 10 Applying the previous technique to construct the modulus contour map for the study area necessitates the presence of the following: - Water table contour map to detect the value and direction of groundwater flow. - Data of pumping tests for a group of wells to get the transmissivity (T) - An iso-salinity contour map for the purpose of water quality. The water table contour map (Fig.21) is taken after Gedamy, (2004). To get the transmissivity, pumping test analysis is carried out for 12 drilled wells distributed in the study area (Fig. 22). The iso-salinity zonation map (Fig. 2) is drawn using the salinity measurements for the water points. The obtained values of modulus groundwater flow are used to construct a modulus contour map (Fig. 24). It shows that the study area is characterized by successive negative zones and one positive zone. The small changes noticed in the modulus contour values are due to the small storage capacity of the aquifer and poor groundwater flow as a result of low values of transmissivity average 29 /day except wells No 48 and have average 140 Fig. 21 Water level contour map. Fig. 22 Transmissivity contour map of alluvial aquifer. Fig. 2 Iso-Salinity zonation map of the study area. Fig. 24 Modulus contour map of the study area.

11 Fifteenth International Water Technology Conference, IWTC , Alexandria, Egypt 11 Negative modulus value zone means that the amount of subsurface recharge along the upstream contour is less than the amount of subsurface discharge along the preceding downstream contour. This is due to additional vertical recharge for the aquifer in the area between each successive two contours. This zone usually has high efficiency and considerable water replenishment. Positive modulus value zone means that the amount of subsurface recharge along the upstream contour is more than the amount of subsurface discharge along the preceding downstream contour. This zone has medium efficiency and medium water replenishment. The estimated quantity of recharge for the total area can be calculated by applying the following equation: Total recharge = Recharge for the sub-area * Total area Sub-area Table (4 ) : Shows the calculation of the total amount of recharge to the study aquifer. Discharge at the up-stream Table (4 ) : Recharge calculation of the investigated area. Discharge at the downstream contour Sub-area Between The two Recharge For the Subarea Total Area (KmP2 P) Recharge for the total area (1) (2) () (4) = (2) (1) () (6)= According to the above calculation, the recharge to the water bearing formation is about 8 * 10 P6P mpp (2000). It is clear that the aquifer is quantitatively limited. By matching the salinity zonation map with water level contour map and modulus contour map (Figure2), as well as, the matching of depth to water zonation map with water level and modulus contour map (Figure26), the northern and northwestern portions are characterized by reasonable aquifer capacity in frame of scientific groundwater management. On the other hand, the eastern and southern portions reflect limited quantitatively and qualitatively aquifer. Fig. (2) : Matching map of modulus water level contour map with Salinity zonation map.... Fig.(26): Matching map of modulus and water level contour maps with Depth to water map.

12 Fifteenth International Water Technology Conference, IWTC , Alexandria, Egypt 12 CALCULATION OF WATER BUDGET FOR THE WATER BEARING FORMATION BY APPLYING PROCESSING MODFLOW FOR WINDOWS (PMWIN) ( Steady state flow simulation): The application of Modflow, a modular three dimensional finite difference groundwater of U. S. Geological Survey to the description and prediction of the behavior of groundwater systems have increased significantly over the last few years. The original version of Modflow 88 (McDonald and Harbaugh, 1988) or Modflow 96 ( Harbaugh and McDonald, 1996 a, 1996 b) can simulate the effects of wells, rivers, drains, head dependent boundaries, recharge and evapotranspiration. These codes are called packages, models, or simply programs These packages are integrated with Modflow, where, each package deals with a specific feature of the hydrologic system to be simulated, such as wells, recharge or river. The transport model PMPATH (Chiang and Kinzelbach, 1994 & 1998), the solute transport model MTD (Zheng, 1990), MTDMS (Zheng and Wang, 1998) and the parameter estimation /day. programs (PEST) (Doherty etal, 1994) and UCODE (Poeter and Hill, 1998) use this approach. The solute transport model MOCD (Konikow etal, 1996) and the inverse model Modflow (Hill, 1992) are integrated with Modflow. Both codes use Modflow as a function for calculation flow fields. The Processing Modflow For Windows (PMWIN) is an integrated simulation system for modeling groundwater flow and transport processes with Modflow 88, Modflow 96, PMPATH, MTD, MTDMS, MOCD, PEST and UCODE. Parameters of model Basic parameters, which were measured during the study, are tabulated in Table and the calculated water budget is shown in Table 6. According to the water level contour (Figure 21), the east west boundaries are considered no flow boundary, while, the southern and northern are considered fixed hydraulic heads (Figure 27). Table Model parameters. Symbol Description Value Unit T Transmissivity / sec. H.K Horizontal hydraulic conductivity m / sec. V.K Vertical hydraulic conductivity m/sec. φ Effective Porosity 24 % Top of layer 20 m Bottom of layer 0.0 m Recharge x10 m/ sec. Pumping rate / sec.

13 Fifteenth International Water Technology Conference, IWTC , Alexandria, Egypt 1 Table 6 Calculation of the water budget for the study aquifer (2008) ============================================================================== WATER BUDGET OF THE WHOLE MODEL DOMAIN : FLOW TERM IN OUT IN-OUT STORAGE E E E+00 CONSTANT HEAD E E E+06 WELLS E E E+00 DRAINS E E E+00 RECHARGE E E E+06 ET E E E+00 RIVER LEAKAGE E E E+00 HEAD DEP BOUNDS E E E+00 STREAM LEAKAGE E E E+00 INTERBED STORAGE E E E+00 MULTI-AQIFR WELL E E E+00 SUM E E E+02 Fixed-head boundary = 4m N No-Flow Boundary 20 km No-Flow Boundary 20 km Fixed-head boundary = 1m 20 km Fig. 27 Schematic diagram of model area (Showing distribution of productive wells). 4 Fixed-head boundary = 1m 20 km

14 Fifteenth International Water Technology Conference, IWTC , Alexandria, Egypt 14 CONCLUSSION: 1- The hydraulic parameters of the investigated aquifer reflect wide range of Transmissivity 4 /day 1787 /day for alluvial aquifer, while 144 /day 90 /day for Marine Kurkar aquifer respectively. 2- The Modulus contour map reflects that the northern and northwestern portions are characterized by reasonable aquifer capacity in frame of scientific groundwater management, while, the eastern and southern portions reflect limited quantitatively and qualitatively aquifer. - Due to the depths of groundwater (46.1 m to 10 m from the ground surface), the rainfall replenishment is nearly absent. On the other hand, the buried channels may represent the main source of groundwater recharge. 4- The safe yield of the aquifer should be protected by decreasing the number of pumping wells for proper utilization of groundwater. - According to the groundwater potentiality, the modern irrigation system must be taken into consideration for new reclaiming areas. 6- Periodical monitoring is recommended to determine any changes in water level and water quality. 7- It s advisable to choose new plants species which need low quantity of water and can overcome water salinity. 8- As a result of previous items 2, 4 and 7 pumping rates of productive wells should be decreased. 9- Field water well design criteria should be taken into consideration to achieve good management including minimizing well losses, developing well productivity and efficiency, and to keep wells working for long possible time without failure. 9- Observation test wells are essential for periodical monitoring of groundwater level fluctuation 10- The distance between each two successive production wells should not be less than 00 m in order to minimize the cone of depression of ground water level. 11- Establishing of data base and updating of the model input data is highly recommended to improve the model results. REFERENCES: Chiang, W.- H. and W. Kinzelbach, PMPATH 98. "An advective ransport model for Processing Modflow and Modflow" Doherty, J., L. Brebber and P. Whyte, PEST Model independent parameter estimation. User s manual. Watermark Computing. Australia, Gedamy, Y. R. A., Geochemical studies of the groundwater in North-East Sinai area, Egypt. Ph.D. Thesis, Fac. Sci., Ain Shams Univ., Cairo, Egypt, 821p, Harbaugh, A.W.and M.G. McDonald, User s documentation for MODFLOW 96, an update to the U.S. Geological Survey modular finite difference groundwater flowmodel, USGS Open File Report 96 48, 1996 a.

15 Fifteenth International Water Technology Conference, IWTC , Alexandria, Egypt 1 Harbaugh, A. W. and M. G. McDonald, Programmer s documentation for MODFLOW 96, an update to the U.S.Geological Survey modular finite difference groundwater flow model, USGS Open File Report , 1996 b. Hammad, F., A.: "Geomorphological and Hydrogeological aspects of Sinai Peninsula, A.R.E., Annals of the Geological Survey of Egypt, v. X, p , Hill, M.C., MODFLOW/P A computer program for estimating parameters of a transient, three dimensional, groundwater flow model using nonlinear regression, U.S. Geological Survey, Open File report , Japan International Cooperation Agency "North Sinai groundwater resources study in the Arab Republic of Egypt. Final report submitted to the Research Institute for Water Resources, Ministry of Public Works and Water Resources, Cairo, Egypt, 207p, Konikow, L. F., D. J. Goode and G. Z. Homberger, A three dimensional method of characteristics solute transport model. U.S. Geological Survey. Water Resources Investigations report , McDonald, M. G. and A.W.Harbaugh, MODFLOW, A modular three dimensional finite difference groundwater flow model, U. S. Geological Survey, open file report 8 87, Chapter A1, Research Institute for Water Resources (RIWR), Groundwater management study in El Arish Rafah plain area. Phase 1, Vol.11, Cairo, Egypt, 166p, 988. Research Institute for Water Resources (RIWR), Sinai water resources study (phase II). Internal Report, 191p, Rofail, N.H., "The groundwater modulus map on the Nile Delta, High Technical. Education Conference, Brne Czechoslovakia, no. 1-2, pp , Sewidan, A. S. and N.H.Rofail "Groundwater modulus map of El Qasr area Western Desert, Mediterranean Coastal Zone. Arab Engineering Congress, Cairo, 8p, Shata, A. A. Structural development of the Sinai Peninsula, Egypt. Bull. Desert Institute, Cairo, Egypt, Vol. 6, No.2, pp , 196. Taha, A. A. M. Geology of the groundwater supplies of El Arish-Rafah area, northeast Sinai, U.A.R.. M.Sc. Thesis, Fac. Sci., Cairo Univ., Egypt. 129p, Todd, D. K. Groundwater hydrology. 2nd edition, John Wiley and Sons Interscience, New York, U.S.A., 6p, 199.

16 Fifteenth International Water Technology Conference, IWTC , Alexandria, Egypt 16 Zheng, C., MTD, a modular three dimensional transport model, S.S. Papadopulos & Associates, Inc., Rockville, Maryland, Zheng, C. and P.P. Wang, MTDMS, A modular three-dimensional multispecies transport model for simulation of advection, dispersion and chemical reactions of contaminants in groundwater systems. Documentation and user s guide. Departments of Geology and Mathematics, University of Alabama, 1998.

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